Tag: Cathleen

Look, Look Again, Then Think

On By rolcottIn Astronomy, UncategorizedLeave a comment

Cathleen and I are sharing scones and memories when Vinnie trundles up to our table. “Glad I got you two together. I just ran across a couple news items and I need some explanations.”

“Astronomy AND Physics in the same news items? Do tell.”

“They’re only one paragraph each and read like someone wrote ’em before their morning coffee. They’re both about that big black hole they’ve been taking pictures of.”

“The one in our galaxy or the M87* supermassive black hole in the Messier‑87 galaxy?”

“The second one, Cathleen. This item says it shot out a jet traveling faster than light.”

<sigh> “Pop‑sci journalism at its worst, right, Sy? I know the work that’s based on and the academic reports don’t say that. Good observations leading to less flamboyant conclusions.”

“Maybe it was supposed to be a bigger article but the editors cut it down badly. That happens. I’m sure it’s not really a superluminal jet—”

“Superluminal’s faster‑than‑light, right?”

“Right, Vinnie. Sorry to get technical. Anyway, it’s an illusion.”

“Ah geez, it’ll be frames again, right?” <eyes suddenly open wide> “Wait, I got it! I betcha it’s about the time difference. Take a blob in that jet, it’s flying out at near lightspeed. Time dilation happens when relativity’s in the game, me and Sy talked about that, so blob‑frame seconds look like they take longer than ours do. We see the blob cramming a lightsecond of distance traveled into less than one of our seconds and that’s superluminal. Am I right, Sy?”

“Right answer to a different question, I’m afraid. You’re straight on the time dilation but it doesn’t apply to this situation. Something happening within the blob’s frame, maybe a star blowing up or something weird metabolizing in there, Special Relativity’s time distortion hijinks would show us that action taking place in slow motion. But this superluminal blob claim hinges on how the blob’s whole frame moves relative to ours. That motion isn’t superluminal but it can look that way if conditions are right. As I understand it, the M87* jet qualifies. Your bailiwick rather than mine, Cathleen.”

“Actually it is a frames thing, Vinnie, but timeframes, not spacetime. Those blobs move too slowly in our sky to watch in real time. We take snapshot A and then maybe a few years later we take snapshot B and compare. Speed is the ratio of distance to time. We need the A‑B distance in 3‑D space to compare to the known time between snapshots. But we can’t see the blob’s trajectory in 3‑D. All we can capture is its 2‑D arc C‑B across an imaginary spherical shell we call the sky. If the M87* jet were perpendicular to our line of sight the C‑B image on the sky‑sphere would match the 3‑D path. Multiply the image’s angle in radians by the distance to M87* and we’re done.”

“We’re not done?”

“Nope. This jet points only 20° away from our direct line of sight. I’ll spare you the trigonometry and just say that distance A‑B is about 3 times longer than C‑B.”

“So we measure C‑B, triple the angle and multiply by the M87* distance. No problem.”

“Problem. That tripling is what makes the blob’s A‑B journey appear to go faster than light. Three times 0.4c equals 1.2c. But you missed something important. Your arithmetic assumed you could use a simple ‘M87* distance’. Not in this case, because the blob moves towards us at close to lightspeed. Visualize two concentric sky‑spheres. The outer one’s radius runs from us to the blob’s location at A‑time. The inner sphere’s radius runs to the blob’s location at B‑time. The B‑sphere is our reference frame. The light we saw at A‑time had to travel from the outer sphere to the inner one before we could register the C‑B image.”

“Can’t be very far.”

“We’re talking years at lightspeed, so lightyears, so significant. A properly illusion‑free A‑B travel calculation must include the A‑C travel time in the denominator of the distance/time ratio. The true kilometers per second come out well below lightspeed. Oh, and relativity’s not involved.”

“Dang, Cathleen, it was such a cool illusion.”

~ Rich Olcott

Sharpening The Image

On By rolcottIn Astronomy: Stellar Science, Astronomy: Techniques, UncategorizedLeave a comment

“One coffee, one latte and two scones, Cal. Next time is Cathleen’s turn. Hey, you’ve got a new poster behind the cash register. What are we looking at?”

“You like it, Sy? Built the file myself from pics in my astronomy magazines, used the Library’s large‑format printer for the frameable copy. Came out pretty well, didn’t it, Cathleen?”

“Mm‑hm. Sy, you should recognize the pebbly-looking one. It’s granules at the bottom of the Sun’s atmosphere. The image came from the Inouye Solar Telescope at Haleakala Observatory on Maui, probably Earth’s best ground‑based facility for studying the Sun. I showed the image to your niece in that phone call. For scale, those granules of super‑heated rising gas are each about the size of Texas.”

“My magazine article didn’t mention Texas but it said there’s about ten million granules. What it was mostly about was the IST and its resolution. Those edges in the picture are as narrow as 18 miles across. It’s that good ’cause the beast has a 4‑meter mirror, which used to be amazing, but they made it even better with active and adaptive optics.”

“Hmm. It’s obvious that the bigger the mirror, the better it is for catching photons. If someone’s going to build a big mirror they’re going to put it behind a big aperture, which is important for resolving points that are close together. But what are ‘active and adaptive optics’ and why did you say that like they’re two different things?”

” ‘Cause they are two different things, Sy. Different jobs, different time‑scales. Gravity here on Earth can make a big mirror sag, and the sag changes depending on where the machine is pointed and maybe part of it gets the wrong temperature. Active optics is about keeping the whole mirror in the right shape to focus the photons where they’re supposed to go. There’s a bunch of actuators rigged up to give adjustable support at different points behind the mirror. The astronomer tells the system to watch a certain guide point and there’s a computer that directs each actuator’s pushing to sharpen the point’s image.”

“And adaptive optics?”

“That’s about solving a different problem. Stars twinkle, right, and the reason they twinkle is because of the atmosphere. One part refracts light one way, another part maybe warmer or with different humidity sends the light another way. Everything moves second to second. By the time a light‑wave gets down to us it’s been jiggled a lot. Adaptive optics is a small mirror, also with a lot of actuators, placed up in the light path after the primary mirror. Again with a guide point and a computer, the little mirror’s job is to cancel the jiggles so the scope’s sensors see a smooth wave. Adaptive works a lot faster than active, which sounds backwards, but I guess active came first.”

“The granules must be in the Sun’s disk somewhere. The other two images look like they’re on the edge.”

“That’s right, Sy. The bottom one is from the Solar Dynamic Observatory satellite a few years ago. That’s not visible light, it’s EUV—”

“EUV?”

“Extreme UltraViolet, light‑waves too short even for hydrogen so it’s mostly from iron atoms heated to millions of degrees. SDO had to be a satellite to catch that part of the spectrum because the atmosphere absorbs it. Of course, up there there’s no need for active or adaptive optics but imaging EUV has its own problems.”

“How tall is that photogenic tree?”

“It’s a prominence. The article said it’s about twenty times Earth’s diameter.”

“What about the pink one?”

“That’s new, Cathleen, from another Maui telescope. Adaptive optics were in play but there’s a problem. If you’re probing inside the corona there’s no fixed guide point. The team focused their adjustment system on corona features where they were a few seconds ago. The article said the process was ‘tricky,’ but look at the results. The loop is about the size of Earth, and those fine lines are about the width of Vancouver Island. They discovered details no‑one’s ever seen before.”

Top left: Schmidt et al./NJIT/NSO/AURA/NSF;
Top right: NSO/AURA/NSF under CC A4.0 Intl license;
Bottom: NASA/SDO

~ Rich Olcott

Snap The Whip

On By rolcottIn Astronomy: Stellar Science, Physics: Electromagnetism, UncategorizedLeave a comment

“You say Alfven invented a whole science, Sy, but his double‑layer structures in plasma don’t look like much compared with the real ground‑breakers like Herschel or Hubble.”

“Your Astronomy bias is showing, Cathleen. The double‑layer thing was only a fraction what he gave to magnetohydrodynamics. To begin with, he dreamed up a new kind of wave.”

“There’s more than light waves, sound waves and ocean waves?”

“Certainly. There’s dozens of different kinds — look up waves in Wikipedia some day. Some move, some make other things move; sometimes things move in the direction the wave does, sometimes crosswise to it. From a Physics perspective waves are about repetition. Something that happens just once, where do you go from there?”

“That used to be Astronomy’s problem — only one solar system with fewer than a dozen planets, only two galaxies we could inspect closely. Now our space telescopes and monster‑mirror ground‑based observatories have given us thousands of planets and billions of stars and galaxies. If we get our classifications right we can follow an object type through every stage of development. It’s almost like watching Chemistry happen.”

“I doubt Susan Kim would agree but I get your point. Anyhow, most waves have a common underlying process. Many systems have an equilibrium condition. Doing something energetic like plucking on a guitar string moves the system away from equilibrium. That provokes some force to restore equilibrium. For the guitar, tension in the wire pulls it straight. Usually the restoration overshoots so the restoring force turns around to act in the opposite direction. That’s when the repetition starts, right?”

“Mm-hm, that’s sound waves in a nutshell. Ocean waves, too, because gravity’s the restoring force fighting with the wind to pull things flat.”

“Same idea. Well, Alfven’s first trick was to demonstrate that in a plasma or any conducting medium, a magnetic field acts like that guitar string. The field’s equilibrium configuration is straight and smooth. If you perturb the medium somehow to put a bend or kink in the field, magnetic tension kicks in to restore equilibrium. Waves restored by magnetic fields are important enough that they’re now called Alfven waves in his honor.”

“First trick, mmm? There’s more?”

“Yup, an old one he borrowed from Maxwell — the flux tube. Maxwell worked before atoms were a conceptual thing. He thought about magnetism in terms of immaterial ‘lines of force’ that followed the rules laid out in his equations. Think of grabbing a handful of barely cooked spaghetti, still mostly stiff.”

“Yuck.”

“You’re wearing gloves, okay? The point is, you’ve got a more‑or‑less cylindrical bundle of parallel strands. Pretend each strand is a line of magnetic force. Maxwell’s rules say the number of lines of force, the total magnetic flux, coming out one end of the bundle exactly equals the flux that went in the other end. There’s no sourcing or destroying magnetic flux in between.”

“What if I squeeze real hard?”

“Nope. The flux per unit area intensifies — that’s called ‘the pinch effect’ and particle beam folks love it — but the total flux stays the same. Here’s where it gets interesting. Alfven showed that if the flux tube passes through a plasma or other conducting medium, the medium’s charged particles get frozen into the field. Waggle the field, you waggle the particles. Now put that together with his waves.”

“Oh, that’s what those guys have been talking about! There’s a slew of recent papers built on observations from the Parker Solar Probe mission. One of the biggest outstanding problems in solar physics is, how can the corona, the outermost layer of the Sun’s atmosphere, be millions of degrees hotter than the 6000‑degree photosphere beneath it? Well, PSP and other satellite missions have recorded many observations where the ambient magnetic field suddenly flipped from one direction to its near‑opposite. It’s like the probe had flown through a flux tube zig‑zag in space.”

“Those sharp angles indicate a lot of pent‑up magnetic tension.”

“Absolutely! Now imagine those zig‑zags in the crowded chaos inside the Sun’s atmosphere, colliding, criss‑crossing, disconnecting, reconnecting, releasing their magnetic flux energy into frozen‑in particles that aren’t frozen any more. What do you get, Sy?”

“Immense amounts of kinetic energy. Hot times, indeed”

~ Rich Olcott

Why Those Curtains Ripple

On By rolcottIn Astronomy: Planetary Science, Physics: Electromagnetism, UncategorizedLeave a comment

I’m in the scone line at Cal’s Coffee when suddenly there’s a too‑familiar poke at my back, a bit right of the spine and just below the shoulder blade. I don’t look around. “Morning, Cathleen.”

“Morning, Sy. Your niece Teena certainly likes auroras, doesn’t she?”

“She likes everything. She’s the embodiment of ‘unquenchable enthusiasm.’ At that age she’s allowed.”

“It’s a gift at any age. Some of the kids in my classes, they just can’t see the wonders no matter how I try. I show them aurora photos and they say, ‘Oh yes, red and green in the sky‘ and go back to their phone screens. Of course there’s no way to get them outside late at night at a location with minimal light pollution.”

“I feel your pain.”

“Thanks. By the way, your aurora write-ups have been all about Earth’s end of the magnetic show. When you you going to do the rest of the story?”

“How do you mean?”

“Magnetism on the Sun, how a CME works, that sort of thing.”

“As a physicist I know a lot about magnetism, but you’re going to have to educate me on the astronomy.”

Plane‑polarized Lorentz (electromagnetic) wave
 Electric (E) component is red
 Magnetic (B) component is blue
(Image by Loo Kang Wee and Fu-Kwun Hwang from Wikimedia Commons)
Licensed under CC ASA3.0 Unported

“Deal. You go first.”

<displaying an animation on Old Reliable> “We’ll have to flip between microscopic and macroscopic a couple times. Here’s the ultimate micro — a single charged particle bouncing up and down somewhere far away has generated this Lorentz‑force wave traveling all alone in the Universe. The force has two components, electric and magnetic, that travel together. Neither component does a thing until the wave encounters another charged particle.”

“An electron, right?”

“Could be but doesn’t have to be. All the electric component cares about is how much charge the particle’s carrying. The magnetic component cares about that and also about its speed and direction. Say the Lorentz wave is traveling east. The magnetic component reaches out perpendicular, to the north and south. If the particle’s headed in exactly the same direction, there’s no interaction. Any other direction, though, the particle’s forced to swerve perpendicular to both the field and the original travel. Its path twists up- or downward.”

A charged particle traversing a Lorentz wave

“But if the particle swerves, won’t it keep swerving?”

“Absolutely. The particle follows a helical path until the wave gives out or a stronger field comes along.”

“Wait. If a Lorentz wave redirects charge motion and moving charges generate Lorentz waves, then a swerved particle ought to mess up the original wave.”

“True. It’s complicated. You can simplify the problem by stepping back far enough that you don’t see individual particles any more and the whole assembly looks like a simple fluid. We’ve known for centuries how to do Physics with water and such. Newton invented hydrodynamics while battling the ghost of Descartes to prove that the Solar System’s motion was governed by gravity, not vortices in an interplanetary fluid. People had tried using Newton‑style hydrodynamics math to understand plasma phenomena but it didn’t work.”

<grinning> “I don’t imagine it would — all that twistiness would have thrown things for a loop.”

“Haha. Well, in the early 1940s Swedish physicist Hannes Alfven started developing ideas and techniques, extending hydrodynamics to cover systems containing charged particles. Their micro‑level electromagnetic interactions have macro‑level effects.”

“Like what?”

“Those aurora curtains up there. Alfven showed that in a magnetic field plasmas can self‑organize into what he called ‘double layers’, pairs of wide, thin sheets with positive particles on one side against negative particles in the other. Neither sheet is stable on its own but the paired‑up structure can persist. Better yet, plasma magnetic fields can support coherent waves like the ones making that curtain ripple.”

“Any plasma?”

“Sure.”

“Most of the astronomical objects I show my students are associated with plasmas — the stars themselves, of course, but also the planetary nebulae that survive nova explosions, the interstellar medium in galactic star‑forming regions, the Solar wind, CMEs…”

“Alfven said we can’t understand the Universe unless we understand magnetic fields and electric currents.”

~ Rich Olcott

Old Sol And The Pasta Pot

On By rolcottIn Astronomy: Stellar Science, UncategorizedLeave a comment

<chirp, chirp> “Excuse me, folks, it’s my niece. Hello, Teena.”

“Hi, Uncle Sy. What’s a kme?”

“Sorry, I don’t know that word. Spell it.”

“I’ve never seen it written down. Brian says the Sun’s specially active and gonna spit out a kme that’ll bang into Earth and knock us out of our orbit.”

“Ah, that’s a C‑M‑E, three separate letters. It stands for Coronal Mass Ejection. As usual, Brian’s got some of it right and much of it wrong. The right part is that the Sun’s at the peak of its 11‑year activity cycle so there’s lots of sunspots and flares—”

“He said flares, too. They’re super bright and could cook an Astronaut and it’d happen so fast we won’t have any warning.”

“Once again, partially right but mostly wrong. Here, let me give you to Cathleen who can set you straight. Cathleen, did you catch the conversation’s drift?”

<phone‑pass pause> “Hello, Teena. I gather you’re upset about solar activity?”

“Hi, Dr O’Meara. Yes, my sorta‑friend Brian likes to scare me with what he brings back from going down YouTube rabbit holes. I don’t really believe him but. You know?”

“I understand. Rabbit holes do tend to collect rubbish. Here, let me send you a diagram I use in my classes.” <another pause> “Did you get that?”

“Mm‑hm. Brian showed me a picture like that without the cut‑out part because he was all about the bright flashes.”

“Of course he was. I’ll skip the details, but the idea is that the Sun generates its heat and light energy deep in the reaction zone. Various processes carry that energy up through other zones until it hits the Sun’s atmosphere. You’ve watched water boil on the stove, surely.”

“Oh, yes. Mom put me in charge of doing the pasta last year. I don’t care what they say, a watched pot does eventually boil if there’s enough heat underneath it. I experimented.”

“Wonderful. That process, heat rising into a fluid layer, works the same way on the Sun as it does in your pasta pot. Heat ascends through the fluid but it doesn’t do that uniformly. No, the continuous fluid separates into distinct cells, they’re called Bénard cells, where hot fluid comes up the center, spreads out and cools across the top and then flows down the cell’s outer boundary.”

“That’s what I see happen in the pot with low water and low heat just before the bubbling starts.”

High-res image of the Sun’s surface by DKIST.
Credit: NSO/AURA/NSF, under CC A4.0 Intl license.

“Right, bubbling will disturb what had been a stable pattern. The cells in the Sun’s surface, they’re called granules, continually rise up to the surface and crowd out neighbors that have cooled off enough to sink or disappear.”

“Funny to say something on the Sun is cool.”

“Relatively cool, only 4000K compared to 6000K. But the Sun has bubbles, too. The granules run about 1500 kilometers wide and last only a quarter‑hour. There’s evidence they’re in top of a supporting layer of supergranules 20 times wider. Or maybe the plasma’s magnetic field is patchy. Anyhow, the surface motion is chaotic. Occasionally, especially concentrated heat or magnetic structure punches out between the granules. There’s a sudden huge release of superhot plasma, a blast of electromagnetic energy radiating out at all frequencies — that’s one of Brian’s flares. Lasts about as long as the granules.”

“That’s what could cook an astronaut?”

“Not really, The radiation’s pretty spread out by the time it’s travelled 150 million kilometers to us. The real danger is from high‑energy particle storms that travel along the Sun’s magnetic field lines. Space crews need to take shelter from them but particle masses travel slower than light so there’s several hours notice.”

“So what about the CMEs?”

“They’re big bubbles of plasma mass that the Sun throws off a few times a year on average. Maybe they come from ultra‑flares but we just don’t know. Their charged particles and magnetic fields can mess up our electronic stuff, but don’t worry about their mass. If a CME’s entire mass hit us straight on, it’d be only a millionth of a millionth of Earth’s mass. We’d roll on just fine.”

~ Rich Olcott

Caged But Free

On By rolcottIn Astronomy, UncategorizedLeave a comment

Afternoon coffee time. Cal waves a handful of astronomy magazines at us as Cathleen and I enter his shop. “Hey, guys, there’s a ton of black hole stuff in the news all of a sudden.”

Cathleen plucks a scone from the rack. “Not surprised, Cal. James Webb Space Telescope looks harder and deeper than we ever could before and my colleagues have been feasting on the data. Black holes are highly energetic so the most extreme ones show up well. The Hubble and JWST folks find new extremes every week.”

Cal would be disappointed if I didn’t ask. “So what’s the new stuff in there?”

<flipping through the magazines> “This seems to be quasar jet month. We’ve got a new champion jet and this article says M87’s quasar makes novas.”

“Remind me, Cathleen, what’s a quasar?”

“A quasi‑stellar object, Sy, except we now know it’s a galaxy with a supermassive black hole—”

“I thought they all had super‑massives.”

“Most do, but these guys are special. For reasons researchers are still arguing about, they emit enormous amounts of energy, as much as a trillion average stars. Quasar luminosity is more‑or‑less flat all across the spectrum from X-rays down as low as we can measure. Which isn’t easy, because the things are so far away that Universe expansion has stretched their waves by z‑factors of 6 or 8 or more. We see their X‑ray emissions in the infrared range, which is why JWST’s optimized for infrared.”

“What does ‘flat’ tell you?”

“Sy’d give a better answer than I would. Sy?”

“Fun fact, Cal. Neither atoms nor the Sun have flat spectra and for the same reason: confinement. Electromagnetic waves come from jiggling charges, right? In an atom the electron charge clouds are confined to specific patterns centered on the nucleus. Each pattern holds a certain amount of energy. The atom can only move to a different charge pattern by emitting or absorbing a wave whose energy matches the difference between the pattern it’s in and some alternate pattern. Atomic and molecular spectra show peaks at the energies where those transitions happen.”

“But the Sun doesn’t have those patterns.”

“Not in the stepped energy‑difference sense. The Sun’s made of plasma, free electrons and nuclei all bouncing off each other, moving wherever but confined to the Sun’s spherical shape by gravity. Any particle that’s much more or less energetic than the local average eventually gets closer to average by exchanging energy with its neighbors. Free charged particles radiate over a continuous, not stepwise, spectrum of energies. The free‑particle combined spectrum has a single peak that depends on the average temperature. You only get flat spectra from systems that aren’t confined either way.”

“What I get from all that is a jet’s flat spectrum says that its electrons or whatever aren’t confined. But they must be — the things are thin as a pencil for thousands of lightyears. Something’s gotta be holding them together but why no peaks?”

“Excellent question, Cal. By the way, jets can be even longer than you said. I’ve read about your champion jet. It extends 23 million lightyears, more than a hundred times the width of the Milky Way galaxy. Straight as a string, no kinks or wiggles during a billion years of growth. I think what’s going on is that the charged particles are confined side‑to‑side somehow but they’re free to roam along the jet’s axis. If that’s the case, the flat‑spectrum light ought to be polarized. I’m sure someone is working on that test now. Your thoughts, Sy?”

“As a physicist I’m interested in the ‘somehow.’ We only know of four forces. The distances are too big for weak and strong nuclear forces. Gravity’s out, too, because it acts equally in all directions, not just crosswise to the axis. That leaves electromagnetic fields in some super‑strong self‑reinforcing configuration. The particles must be spiraling like mad about that central axis. I’ll bet that explains Cal’s quasar galaxy concentrating novae close to its SMBH jet axis. A field that strong could generate enough interference to wreak havoc on an unstable star’s plasma.”

Hubble’s view of the M87 galaxy and jet
Credit NASA and the Hubble Heritage Team (STScI/AURA)

~ Rich Olcott

The Oldest Clock Ticks Slowest

On By rolcottIn Astronomy: Techniques, Chemistry, UncategorizedLeave a comment

<Cliff‑hanger Cathleen strikes again> “How can you even measure a 2‑million year half‑life?”

Kareem’s right back at her. “What’s a half‑life?”

“Start a clock, weigh a sample, wait around for a while and then weigh it again to see how much is still there. When half of it’s gone, stop the clock and you’ve measured a half‑life. Simple.”

“Simple but not that simple or maybe a bit simpler. For one thing, you don’t have to wait for a full half‑life. For spontaneous radioactivity, all you have to know is the interval and whatever fraction disappeared. There’s a nice equation that ties those two to the half‑life.”

“Spontaneous? Like there’s another kind?”

“Stimulated radioactivity. That’s what nuclear reactors do — spew neutrons at uranium‑235 atoms, for instance, transmuting them to uranium‑236 so they’ll split into krypton and barium atoms and release energy and more neutrons. How often that happens depends on neutron concentration. Without that provoking push, the uranium nuclei would just split when they felt like it and that’s the natural half‑life.”

“Wait. I know that curve, it’s an exponential. Why isn’t e in the equation?”

“It could be. Would you prefer e-0.69315*t/half‑life? Works just as well but it’s clumsier. Base‑2 makes more sense when you’re talking halves. Usually when you say ‘exponential’ people visualize an increase. Here we’re looking at a decrease by a constant percentage rate but yeah, that’s an exponential, too. You get a falling curve like that from a Geiger counter and you’re watching counts per minute from someone’s thyroid that’s been treated with iodine‑131. Its 8‑day half‑life is slow enough to track that way. Really short half‑lives I don’t know much about; I care about the slow disintegraters that are either primordial or generated by some process.”

“Primordial — that means ‘back to the beginning’, which in your specialty would mean the beginning of the Solar System. We’re pretty sure the Sun’s pre‑planetary disk was built from dust broadcast by stars that went nova. Isotopes in the dust must be the primordial isotopes, right? Which ones are the other kind?”

“Mmm, aluminum‑26 is a good example. The half‑life equation still applies even for million‑year intervals. Half‑life of aluminum‑26 is about 0.7 million years and it decays to magnesium‑26. Whatever amount got here from the stars would have burnt down to a trillionth of that within the first 30 million years or so after arrival. Any aluminum‑26 we find today couldn’t be primordial. On the other hand, cosmic rays can smack a proton and neutron out of a silicon‑28 nucleus and voila! a new aluminum‑26. There’s a steady rain of cosmic rays out in space so there’s a steady production of aluminum‑26 out there. Not here on Earth, though, because our atmosphere blocks out most of the rays. Very nice for us geologists who can compare measured aluminum‑26 to excess magnesium‑26 to determine when a meteorite fell.”

“Excess?”

“Background magnesium is about 10% magnesium‑26 so we have subtract that to get the increment which came from aluminum‑26. A lot of the arguments in our field hinge on how much of which isotope is background or was background when a given rock formed. That’s one reason you see so much press about tiny but rugged zircons. They’re key to uranium‑lead dating. Crystallizing zirconium silicate doesn’t allow lead ions into its structure but it happily incorporates uranium ions. Uranium‑235 and uranium‑238 both decay to crystal‑trapped lead, but each isotope goes to a different lead isotope and with a different half‑life. The arithmetic’s simpler and the results are more definitive when you know that the initial lead content was zero.”

“So that aluminum‑magnesium trick’s not your only tool?”

“Hardly. The nuclear chemists have given us a long list of isotope chains, what decays to what with what half‑life and how much energy the radiating particle gets. Nuclei flit between quantum energy levels just like atoms and molecules do, except a spectrum of alpha or beta particles is a different game from the light‑wave spectrum. Tell me a radiated particle’s energy and I can probably tell you which isotope spat it out and disappeared.”

“Your ladder rungs are Cheshire Cat grins.”

~~ Rich Olcott

The Not-so-dangerous Banana

On By rolcottIn Astronomy: Techniques, Physics: Quantum Mechanics, UncategorizedLeave a comment

“Y’know, Cathleen, both our ladders boil down to time. Your Astronomy ladder connects objects at different times in the history of the Universe. My Geology ladder looks back into the Solar System’s history.”

“As an astronomer I normally think of parsecs or lightyear distances but you have a point, Kareem. Edwin Hubble linked astronomical space with time. Come to think of it, my cosmologist colleagues work almost exclusively in the time domain, like ‘T=0 plus a few lumptiseconds.’ Billions of years down to that teeny time interval — how does your time ladder compare?”

“Lumptiseconds out to a hundred trillion times the age of the Universe. I win.”

“C’mon, Kareem.”

“No, really, Sy. My ladder uses isotopes. Every carbon atom has 6 protons in the nucleus, right? Carbon‑12 adds 6 neutrons and it’s stable but another isotope, carbon‑14, has 8 neutrons. It’s radioactive — spits out an electron and becomes stable nitrogen‑14 with 7 and 7. Really heavy isotopes like uranium‑238 spit out alpha particles.”

“Wait, if carbon‑14 spits out an electron doesn’t that make it a carbon ion?”

“Uh‑uh, Cathleen, the electron comes out of the nucleus, not the electron cloud. It’s got a hundred thousand times more energy than a chemical kick could give it. Sy could explain—”

“Nice try, Kareem, this is your geologic time story. Let’s stay with that.”

“If I must. So, the stable isotopes last forever, pretty much, but the radioactive ones are ticking bombs with random detonation times.”

“What’s doing the ticking? Surely there’s no springs or pendulums in there.”

“Quantum, Cathleen. Sy’s trying to stay out of this so I’ll give you my outsider answer. I picture every kind of subatomic particle constantly trying to leave every nucleus, butting their little heads bazillions of times a second against walls set up by the weak and strong nuclear forces. Nearly every try is a bounce‑back, but one success is enough to break the nucleus. Every isotope has its own personal set of parameters for each kind of particle — wall height, wall thickness, something like an internal temperature ruling how hard the particles hit the walls. The ticking is those head‑butts; the randomness comes from quantum’s goofy rules somehow. How’s that, Sy?”

Chart by Sjlegg, licensed under CC S-A 3.0 unported

“Good enough for jazz, Kareem. Carry on.”

“Right. So every kind of radioisotope is characterized by what kinds of particle it emits, how much energy each kind has after busting through a wall, and how often that happens in a given sample size. And the isotope’s chemistry, of course, which is the same as every other isotope that has the same number of protons. The general rule is that the stable isotopes have maybe a few more neutrons than protons but nearly every element has some unstable isotopes. The ones with too many neutrons, like carbon‑14, emit electrons as beta particles. They go up a square in the Periodic Table. Too few and they drop down by emitting a positron.”

“All those radioactive stand‑ins for normal atoms. Sounds ghastly. Why are we still here and not all burnt up?”

“First, when one of these atoms decays by itself it’s a lot of energy for that one atom, but the energy spreads out as heat across many atoms. Unless a bunch of atoms crumble at about the same time, there’s only a tiny bit of general heating. The major biological danger from radioactivity comes from spit‑out particles breaking protein or DNA molecules.”

“Mutated, not burnt.”

“Mm‑hm. Second, the radioactives are generally rare relative to their stable siblings. In many cases that’s because the bad guys, like aluminum‑26, have had time to decay to near‑zero. That banana you’re eating has about half a gram of potassium atoms but only 0.012% are unstable potassium‑40. Third, an isotope with a long half‑life doesn’t lose many atoms per unit time. A kilogram of tellurium‑128, for instance, loses 2000 atoms per year. The potassium‑40 in your banana has a half‑life of nearly 2 million years. Overall, it releases only about 1300 beta particles per second producing less than a nanowatt of heat‑you‑up power. Not to worry.”

“Two million years? How do you measure something that slow?”

~~ Rich Olcott

EROs Atop A Ladder

On By rolcottIn Astronomy: Techniques, UncategorizedLeave a comment

“‘That’s where the argument started‘? That’s right up there with ‘Then the murders began.’ Cathleen Cliff‑hanger strikes again.”

<giggling> “Gotcha, Sy, just like always. Sorry, Kareem, we’ve had this thing since we were kids.”

“Don’t mind me, but do tell him what’s awry with the top of your galactic distance ladder.”

“I need to fill you in first about the ladder’s framework. We know the distances to special ‘standard candles’ scattered across the Universe, but there’s oodles of other objects that aren’t special that way. We can’t know their distances unless we can tie them to the candles somehow. Distance was Edwin Hubble’s big thing. Twenty years after Henrietta Swan Leavitt identified one kind of candle, Hubble studied the light from them. The farthest spectra were stretched more than the closest ones. Better yet, there was a strict relationship between the amount of stretch, we call it the z factor, and the candle’s distance. Turns out that everything at the intergalactic scale is getting farther from everything else. He didn’t call that expansion the Hubble Flow but we do. It comes to about 7% per billion lightyears distance. z connects candle spectrum, object spectrum and object distance. That lets us calibrate successive overlapping steps on the distance ladder, one candle type to the next one.”

“A constant growth rate — that’s exponential, by definition. Like compound interest. The higher it gets, it gets even higher faster.”

“Right, Kareem, except that in the past quarter-century we’ve realized that Hubble was an optimist. The latest data suggests the expansion he discovered is accelerating. We don’t know why but dark energy might have something to do with it. But that’s another story.”

“Cathleen, you said the distance ladder’s top rung had something to do with surface brightness. Surface of what?”

“Galaxies. Stars come at all levels of brightness. You can confirm that visually, at least if you’re in a good dark‑sky area. But a galaxy has billions of stars. When we assess brightness for a galaxy as a whole, the brightest stars make up for the dimmest ones. On the average it’ll look like a bunch of average stars. The idea is that the apparent brightness of some galaxy tells you roughly how many average stars it holds. In turn, that gives you a rough estimate of the galaxy’s mass — our final step up the mass ladder. Well, except for gravitational lensing, but that’s another story.”

“So what’s wrong with that candle?”

“We didn’t think anything was wrong until recently. Do you remember that spate of popular science news stories a year ago about giant galaxies near the beginning of time when they had no business to exist yet?”

“Yeah, there was a lot of noise about we’ll have to revise our theories about how the Universe evolved from the Big Bang, but the articles I saw didn’t have much detail. From what you’ve said so far, let me guess. These were new galaxy sightings, so probably from James Webb Space Telescope data. JWST is good at infra‑red so they must have been looking at severely stretched starlight—”

“z-factor near 8″

“— so near 13 billion lightyears old, but the ‘surface brightness’ standard candle led the researchers to claim their galaxies held some ridiculous number of stars for that era, at least according to current theory. How’d I do?”

“Good guess, Sy. That’s where things stood for almost a year until scientists did what scientists do. A different research group looking at even more data as part of a larger project came up with a simpler explanation. Using additional data from JWST and several other sources, the group concentrated on the most massive galaxies, starting with low‑z recent ones and working back to z=9. Along the way they found some EROs — Extremely Red Objects where a blast of infra‑red boosts their normal starlight brightness. The researchers attribute the blast to hot dust associated with a super‑massive black hole at each ERO’s center. The blast makes an ERO appear more massive than it really is. Guess what? The first report’s ‘ridiculously massive’ early galaxies were EROs. Can’t have them in that top rung.”

“Kareem, how about the rungs on your ladder?”

~~ Rich Olcott

One Step After Another

On By rolcottIn Astronomy: Techniques, UncategorizedLeave a comment

Mid-afternoon, time for a coffee break. As I enter Cal’s shop, I see Cathleen and Kareem chuckling together behind a jumble of Cal’s distinctive graph‑lined paper napkins. “What’s the topic of conversation, guys?”

“Hi, Sy. Kareem and I are comparing ladders.”

I look around, don’t see anything that looks like construction equipment.

“Not that kind, Sy. What’s your definition of a ladder?”

“Getting down to definitions, eh, Kareem? Okay, it’s a framework with steps you can climb up towards something you can’t reach.”

“Well, there you go.”

“Not much help, Cathleen. What are you really bantering about?”

“Each of our fields of study has a framework with steps that let us measure something that’d be way out of reach without it.”

“You’ll appreciate this, Sy — our ladders even use different math. The steps on Cathleen’s ladder are mostly linear, mine are mostly exponential.”

“And they’re both finicky — you have to be really careful when using them.”

“And they’ve both recently had adjustments at the top end.”

“I can see the fun, I think. How about some specifics?”

They exchange a look, Kareem gestures ‘after you‘ and Cathleen opens. “Mine’s in astrometry, Sy, the precise recording of relative positions. Tycho Brahe’s numbers were good to a few dozen arcseconds—”

“Arcsecond?”

“1/60 of an arcminute which is 1/60 of a degree which is 1/360 of a full circle around the sky. Good enough in Newton’s day for him to explain planetary orbits, but we’ve come <ahem> a long way since then. The Gaia telescope mission can resolve certain objects down to a few microarcseconds but that’s only half the problem.”

“Let me guess — you have angles but you don’t have distances.”

“Bingo. Distance is astrometry’s biggest challenge.”

“Wait, Newton’s Law of Gravity includes r as the distance between objects. For that matter, Kepler’s Laws use r² and r³. Couldn’t you juggle them around to evaluate r?”

“Nope. Kepler did ratios, not absolute values. Newton’s Law has r² but you can rewrite it as F ² = GMm/r² = G(M/r)(m/r), G times the product of two mass‑to‑distance ratios. Newton’s G is our least‑accurate physical constant and we don’t have good handles on either of those numerators. Before space flight we just had mass ratios like M/m. We only discovered the Moon’s absolute mass when we orbited it with spacecraft of known mass. That’s the lowest rung on our mass ladder. Inside the Solar System we go step by step with orbit ratios. Outside the system everything’s measured relative to Solar mass.”

“I’m getting the ladder idea. So how do you distances?”

“Lowest rung is parallax, like binocular vision. You look at something from two different points a known distance apart. Measure the angle between the sight‑lines. Figure the triangles to get the something’s distance. The earliest example I know of was in the mid‑1700s when astrometers thousands of miles apart on Earth watched Venus cross the Sun’s disk. Each recorded the precise time they saw Venus touch the Sun’s disk. Given the time shift and the on‑Earth distance, some trigonometry gave them the Earth‑Venus distance. That put a scale to Newtonian orbital diagrams. Parallax across the width of Earth’s orbit yielded stellar distances out to thousands of lightyears with Hubble. We expect ten times better from Gaia.”

“That gets you maybe across the Milky Way. What about farther out?”

“Several ingenious variations on the parallax idea, but mostly standard candles.”

“Candles?”

“Suppose you measure the brightness of a candle that’s a known distance away and there’s an equally luminous candle some unknown distance away. Measured brightness falls as the square of the distance, so if the second candle appears half as bright it’s four times the distance and so on. Climbing the cosmic distance ladder is going from one kind of uniformly‑luminous candle to another kind farther away.”

“Such as?”

“We know how brightness relates to bright‑dim‑bright cycle time for several types of variable stars. That gets us out to 30 million lightyears or so. Type I‑a supernovas act as useful candles out to a billion lightyears. Beyond that we can use galaxy surface brightness. That’s where the recent argument started.”

~ Rich Olcott

  • Thanks to Ken Burke for mentioning tellurium‑128’s septillion‑year half‑life.